Book for Physicists
- 1 Welcome
- 2 Introduction to the mathematics of medical imaging
- 2.1 Introduction (Introduction to: Mathematics of Medical Imaging)
- 2.2 Integral Geometry and Integral Transforms
- 2.2.1 Introduction ( Introduction to: Integral geometry))
- 2.2.2 Represenation of a Line and other linear geometrical elements
- 2.2.3 The 2D Radon transform
- 2.2.4 The sinogram
- 2.2.5 The properties of the Radon transform
- 2.2.6 The Hilbert-transform
- 2.2.7 The Digital Radon Transform
- 2.2.8 The Radon Transform in multiple dimensions
- 2.3 Analytical Reconstruction techniques
- 2.3.1 Introduction (Analyitical Reconstruction)
- 2.3.2 The Central Slice Theorem
- 2.3.3 The Filtered Backprojection
- 2.3.4 Relaization of the filtered backprojection
- 2.3.5 Multidimensional Central Slice Theorem and the Fourier Inverson Formula
- 2.3.6 Interpretation of the inverse Radon transform
- 2.3.7 Inverse Radon transfrom with Riesz potentials
- 2.3.8 Filter Design for the Filtered Backprojection
- 2.3.9 3D reconstruction
- 2.4 Algebraic Image Reconstruction
- 2.4.1 Introduction (Introduction to: Algebraic Image Reconstruction)
- 2.4.2 Descrete Base for the reconstruction
- 2.4.3 Non-statistical iterative reconstructions
- 2.4.4 Statistical image reconstruction strategies
- 2.4.5 The ML-EM algorithm
- 2.4.6 The ML-EM algorithm for emission tomography
- 2.4.7 ML-EM variations: MAP-EM,OSEM
- 2.5 The DICOM standard
- 2.5.1 Abstract
- 2.5.2 Introduction (DICOM)
- 2.5.3 A simplified DICOM for beginners
- 2.5.3.1 Introduction to the digital representation of alphanumeric data
- 2.5.3.2 Introduction to the a simplified toy-DICOM file format I (Problems for the reader)
- 2.5.3.3 Introduction to the a simplified toy-DICOM file format II (Solutions of the problems)
- 2.5.3.4 Introduction to the a simplified toy-DICOM file format III
- 2.5.3.5 Introduction to the a simplified 'toy-DICOM' file format IV (Further development: the Value Representation)
- 2.5.4 A few words about the real DICOM format
- 2.5.5 Appendix
- 2.6 Mathematical Methods of Linear Model Based Image Processing Procedures
- 2.6.1 Introduction.
- 2.6.2 Linear Operators
- 2.6.3 Characteristic Input Functions
- 2.6.4 General Input Functions - Fourier Transformation
- 2.6.5 Laplace-Transformation
- 2.6.5.1 Analysis of linear systems in extended frequency space
- 2.6.5.2 Properties and rules of Laplace transformation
- 2.6.5.3 Laplace transformation of characteristic and any other typical functions
- 2.6.5.4 Mathematical description of the system properties functions
- 2.6.5.5 Inverse transformation method for linear invariant systems
- 2.6.5.6 Inverse transformation of the proper rational function
- 2.6.5.7 Transfer Function
- 2.6.5.8 Transfer characteristic function (Modulation Transfer Function MTF)
- 2.6.5.9 Linear shift invariant system description by the step response function
- 2.6.5.10 Relation between the step response function and weighting function of linear shift invariant system
- 2.6.6 Problems (Linear Systems)
- 2.6.7 Theory and basic laws of sampling
- 2.6.8 Planar imaging as a linear system
- 2.6.9 Appendix.
- 2.6.9.1 Theorems, Detailed explanations
- 2.6.9.1.1 Deriving of Fourier Theory, Fourier Series
- 2.6.9.1.2 Description of Fourier series by complex expression
- 2.6.9.1.3 Parzeval theorem
- 2.6.9.1.4 Response function in general case
- 2.6.9.1.5 Deriving of Duhamel Theorem
- 2.6.9.2 Solution of problems
- 2.6.9.1 Theorems, Detailed explanations
- 2.7 Monte Carlo Methods (English)
- 2.7.1 Introduction (introduction to: Monte Carlo Methods)
- 2.7.2 Sampling
- 2.7.3 Sampling the free flight distance
- 2.7.4 Sampling an interaction
- 2.7.5 Detection
- 2.8 References
- 3 Nuclear Medicine for Physicists
- 3.1 Introduction to Nuclear Imaging
- 3.2 Detectors
- 3.2.1 Scintillators
- 3.2.1.1 The Process of Scintillation, Types of Scintillators
- 3.2.1.2 Basic Properties of Scintillators
- 3.2.1.3 SPECT Scintillators
- 3.2.1.4 PET Scintillators
- 3.2.2 PMT (Photomultiplier Tube)
- 3.2.3 Semiconductor Photodetectors
- 3.2.1 Scintillators
- 3.3 Measurement background of position sensitive detection
- 3.4 Gamma Cameras and Gamma Camera Imaging
- 3.5 SPECT Imaging
- 3.5.1 Fundaments of the 3-D Emission Imaging
- 3.5.2 Techniques of Reconstruction
- 3.5.3 Conjugate Projections
- 3.5.4 Imaging Errors
- 3.5.5 Pinhole SPECT
- 3.6 PET Imaging
- 3.7 PET/CT Systems
- 3.7.1 Introduction to PET-CT multi-modality imaging
- 3.7.2 Isotope Production
- 3.7.3 Examination
- 3.7.4 Hardware
- 3.7.5 Standardized Uptake Value (SUV)
- 3.7.6 PET/MRI
- 3.8 Radiation Protection in Nuclear Medicine
- 3.9 References (Nuclear Medicine)
- 4 Fundaments of Digital Image Registration and Image Post-Processing
- 4.1 Digital image registration
- 4.2 Static examinations
- 4.3 Dynamic examinations
- 4.4 Visualization of three dimensional (3D) data
- 4.4.1 General introduction
- 4.4.2 Surface rendering
- 4.4.3 Algorithms
- 4.4.4 Volume rendering
- 4.4.5 Combination of volume and surface rendering
- 4.4.6 Three-dimensional parametric images
- 4.4.7 Corrections
- 4.4.8 Transformations
- 4.5 References (Images)
- 5 Medical Imaging in Radiation Therapy
- 5.1 Radiotherapy: Past and Present
- 5.2 Radiation therapy in Hungary
- 5.3 Treatment planning in teletherapy
- 5.4 Teletherapy Equipment
- 5.4.1 X-Ray Therapy
- 5.4.2 Linear accelerator
- 5.4.3 Other types of accelerators.
- 5.4.4 Cobalt unit for teletherapy
- 5.5 Beam Modification devices in Radiotherapy
- 5.5.1 Wedge
- 5.5.2 Shilding
- 5.5.3 Multileaf collimator
- 5.6 Imaging in Radiotherapy
- 5.7 Intensity modulated radiation therapy (IMRT)
- 5.8 Image Guided Radiation Therapy
- 5.9 Quality Improvement of Patient Care in Radiotherapy
- 5.10 Radiation Sources and Devices in Brachytherapy
- 6 Quality Assurance
- 6.1 Role of International Organisation in Quality Assuranc
- 6.2 Basic concepts of Quality
- 6.3 Quality Assurance of PET Device
- 6.4 Quality Control and Quality Assurance for Teletherapy Equipment
- 6.4.1 Quality Control and Quality Assurance of linear accelerators
- 6.4.2 Checks on standard linear accelerators
- 6.4.2.1 Safety interlocks
- 6.4.2.2 Indicator lights
- 6.4.2.3 Mechanical integrity
- 6.4.2.4 Mechanical alignment checks
- 6.4.2.5 Position of light source
- 6.4.2.6 Optical field indication
- 6.4.2.7 Shadow tray
- 6.4.2.8 Couch movements
- 6.4.2.9 Radiation alignment
- 6.4.2.10 Interpretation of alignment checks
- 6.4.2.11 Flatness and symmetry
- 6.4.2.12 Radiation output measurement
- 6.4.2.13 Beam energy
- 6.4.2.14 Arc therapy
- 6.4.2.15 Selection of checks and check frequencies
- 6.4.2.16 Equipment required
- 6.4.3 Quality Assurance of Treatment Simulators
- 6.4.3.1 Appendix I.
- 6.4.3.2 Appendix II.
- 6.4.3.3 Appendix III.
- 6.5 Technical Quality Assurance and Safety of Diagnostic Radiology Equipment
- 6.5.1 Benefit, terms and first steps of technical quality assurance
- 6.5.2 Regulation of technical quality control of diagnostic radiology equipment
- 6.5.3 Levels and names of tests
- 6.5.4 Preliminaries in Hungary
- 6.5.5 Present status of technical quality control of diagnostic radiology equipment
- 6.5.6 Benefit and lessons of acceptance tests
- 6.5.7 Tests to be performed during acceptance and status testing
- 6.5.8 Testing instrumentation needed for acceptance and/or status testing
- 6.5.9 Problems to be solved and possibilities for steps forward
- 6.5.10 Physical foundations of non-invasive X-ray tube voltage measurement
- 6.5.11 The so-called periodic safety checks
- 6.5.12 Regulation of putting medical devices into circulation in the European Union
- 6.5.13 Rules of radiation protection registration of equipment in Hungary
- 6.5.14 Conformity (conformance) certification of medical devices, including X-ray equipment
- 6.5.15 International standards, relating to safety of diagnostic radiology equipment
- 7 The principles of MRI
- 7.1 Fundamentals
- 7.1.1 History
- 7.1.2 Features
- 7.1.3 In a Nutshell
- 7.2 Spin dynamics
- 7.2.1 About Resonances
- 7.2.2 Classical Description
- 7.2.3 Measurable Signal
- 7.2.4 Spin Echoes
- 7.3 Development of spatial resolution
- 7.3.1 Frequency Encoding
- 7.3.1.1 Gradient Echo
- 7.3.2 Phase Encoding
- 7.3.3 Slice Encoding
- 7.3.4 MR Spectroscopy
- 7.3.1 Frequency Encoding
- 7.4 Contrast Mechanisms
- 7.5 Safety Concerns
- 7.1 Fundamentals
- 8 Ultrasound
- 8.1 Introduction to ultrasound
- 8.2 A-scan
- 8.3 M-mode
- 8.4 B-mode
- 8.5 Three-dimensional Ultrasound
- 8.6 Doppler Ultrasound
- 8.7 Új irányok az ultrahang diagnosztikában
- 8.7.1 Szonoelasztográfia
- 9 The fundamentals of X-ray diagnostics
- 9.1 The Fundamental Interactions between X-rays and Matter
- 9.2 X-ray Sources
- 9.2.1 Radioactive Isotopes
- 9.2.2 The X-ray Tube
- 9.3 X-ray detectors
- 9.3.1 X-ray detection with films
- 9.3.2 Fluorescent screens
- 9.3.3 X-ray detection with sctintillators
- 9.4 Elements of radiology imaging
- 9.5 Data Acquisition for Computed Tomography (CT)
- 9.6 Cone-beam CT
- 9.6.1 Abbreviations
- 9.6.2 Introduction (Cone-Beam CT)
- 9.6.3 Structure of the Cone-beam CT
- 9.6.4 Data acquisition and processing
- 9.6.5 Reconstruction
- 9.6.6 Image quality parameters
- 9.6.7 Dose of the cone-beam CT
- 9.6.8 Possible applications
- 9.6.9 The future of the cone-beam CT
- 9.6.10 References (cone-beam CT)
- 9.7 References (X-ray diagnostics)
- 10 Lorem Ipsum
- 11 Magnetic Resonance Imaging
- 11.1 Theoretical background of magnetic resonance
- 11.1.1 Precession-classical description
- 11.1.2 Precession-quantum mechanical description
- 11.1.3 Rotating reference, RF excitation and resonance
- 11.1.4 Relaxation
- 11.1.4.1 T1 relaxation
- 11.1.4.2 T2 relaxation
- 11.1.4.3 T2* relaxation
- 11.1.5 Signal detection
- 11.1.5.1 Signal demodulation
- 11.1.6 Fundamental pulse sequences
- 11.1.6.1 Free Induction Decay
- 11.1.6.2 Spin Echo
- 11.1.6.3 Inversion Recovery
- 11.1.7 Repeated pulses and contrast
- 11.2 Principles of MR imaging
- 11.2.1 Fundamental concepts of imaging
- 11.2.1.1 Example: 1D imaging of two spots
- 11.2.2 Gradient Echo and Spin Echo imaging
- 11.2.3 Basics of 2D imaging
- 11.2.1 Fundamental concepts of imaging
- 11.3 Fourier Transform and digital sampling
- 11.1 Theoretical background of magnetic resonance